Heat transfer characteristics of thermally driven bioconvective third grade nanofluid flow with thermal radiation over a stretching cylinder

Nanofluids have attracted significant research interest due to their diverse applications in biomedical engineering, energy systems, and thermal management. This study examines the bioconvective flow of a third-grade nanofluid over a stretching cylinder, incorporating non-uniform heat source/sink, magnetic field, activation energy, motile microorganisms, and nonlinear thermal radiation. To enhance the physical relevance of the study, the effects of Joule heating, buoyancy forces, multiple slip conditions and thermophoresis are integrated into the model. Similarity functions are used to simplify the third-grade nanofluid equation into a set of coupled ODEs. Bvp4c routine available in MATLAB is used to solve formulated ODEs numerically with shooting method. The novelty of investigation lies in in examining the combined influences of non-uniform heat sink/source with bioconvection and slip conditions on third-grade nanofluid. The outcomes of fluid parameters, namely, Peclet number, bioconvection Lewis number, reaction parameter, Brownian motion, thermal radiation, heat source and thermophoresis parameter against the velocity of third-grade fluid, temperature profile, the volumetric concentration profile, and microorganism’s concentration function, have been discovered in depth via graphs, tables and literature. The current examination depicts that the speed of fluid decreases for enlarging amount of bioconvection Rayleigh number, buoyancy ratio parameter and magnetic number. Moreover, it is evaluated that temperature of fluid is climbed by varying the amount of thermal radiation parameter, heat generation parameter and thermophoresis parameter, whereas turns down for raised amount temperature slip parameter. The concentration field decreases for higher ranges of Brownian motion and Lewis number, while conflicting whereas turns up for elevated thermophoresis parameter. Greater values of Péclet number diminish the microorganisms’ density field.